Running quick calibration (reduced simulations for testing)...
Starting PoC calibration...
Target detection rate: 0.1
Number of simulations per C_poc: 100
C_poc range: 0.7 to 0.95
Progress: 1/6 - Testing C_poc = 0.700
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 2/6 - Testing C_poc = 0.750
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 3/6 - Testing C_poc = 0.800
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 4/6 - Testing C_poc = 0.850
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 5/6 - Testing C_poc = 0.900
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 6/6 - Testing C_poc = 0.950
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
=== CALIBRATION COMPLETE ===
Optimal C_poc = 0.700
Achieved detection rate = 0.000 (target: 0.100)
Difference from target = 0.100
============================